The sequel to Ultima featured several improvements over the original, such as separate town and world maps, and the concept of traveling through time gates into different eras on Earth. Other than that the gameplay is pretty much the same as in Ultima I, with your single character roaming the land fighting monsters and looking for key items.
In the original Ultima a hero from a certain third rate blue planet orbiting an insignificant yellow sun came to the world of Sosaria and slew the evil wizard Mondain before he could fulfill his dreams of universal domination. Thus peace was brought to Sosaria, and the hero hailed as a champion of the people of all time.
Unfortunately, Mondain happened to have a young apprentice/lover named Minax who is understandably upset over his death. Using her considerable powers, Minax travels through time and space to the hero's homeworld of Earth and instigates a nuclear war, thus serving the dual purpose of working out her frustration as well as erasing the hero from history. Of course, as the hero, this works out rather badly for you, and so with the help of Lord British you must travel through time and somehow find Minax and prevent the events which culminate in the destruction of Earth.